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Weakly approaching sequences of random distributions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2000 (English)Report (Refereed)
Abstract [en]

We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2000. Vol. 37, no 3, 17 p.807-822 p.
Series
Research report / Department of mathematical statistics, ISSN 1401-730X ; 8
Keyword [en]
Weak convergence, weakly approaching sequences, resampling, bootstrap, continuity theorem, Lévy metric, uniform metric
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-87444DOI: 10.1239/jap/1014842838ISI: 000165452900017OAI: oai:DiVA.org:umu-87444DiVA: diva2:709344
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2014-10-21Bibliographically approved

Open Access in DiVA

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